In 1893, H.G. (Herbert George) Wells (Macolm McDowell) is hosting a gathering of friends in his London home, to announce his new invention, a time machine. He exhibits and explains the vehicle to the incredulous group, and says that he will go to the future instead of the past, because he "belongs there." Scotland Yard detectives arrive at the house to warn them that they have pursued Jack the Ripper to the vicinity. The police inspect the physician bag of one of Herbert's guests, Dr. John Leslie Stevenson, and it contains a bloody knife. But Stevenson has vanished - Herbert finds his time machine missing.

But, as he sits in his basement contemplating the situation, the house begins to shake and the machine reappears, as it has a homing device. Wells sees from the controls that John has gone to the year 1979.

He enters the machine and sets off in pursuit of the Ripper, believing that the the year 1979 will prove to be a Utopia. After an exciting trip through time, during which he hears radio waves of historical events, he arrives at his destination. But the machine is in a museum display in San Francisco, having been loaned by the British Museum. He is amazed at the "Wells - A Man Before His Time" exhibition, showing artifacts from his life.

Herbert is overwhelmed by the sights in the city - fashions,architecture, automobiles, a jet in the sky, He goes from bank to bank, hoping to trace John, who, like himself, would have likely exchanged old British pounds for dollars. He eventually finds banker Amy Robbins (Mary Steenburgen), surprised that a woman would be in the position. She confirms that John Stevenson had exchanged currency, and gives Wells the name of the hotel she referred him to. Amy is intrigued by the curiously attired and mannered Herbert, and volunteers to show him the city.

Herbert finds John in the hotel room, and demands that he return to the past with him to face the consequences. John replies that he belongs "here", and flips through TV channels, showing the violence in our modern world (war coverage, pro football, violent cartoons, etc.). John flees the room with Herbert in pursuit, but is struck by a car. At the hospital, Herbert is told that the patient answering to John's description has died.

Herbert and Amy meet for lunch and, although he had written in his time about "free love", he is shocked by her candor about her sex life. Amy gives him a tour of the San Francisco area and they make love in her apartment that night. In the morning, Herbert hears a report on the radio of multiple killings in the city, and realizes that John is still alive.

Back at the bank, John returns to Amy's desk with more currency to exchange. But he figures out that she has tipped off Herbert, and threatens violence if he does not get the key to the time machine. Herbert is forced to explain all to the disbelieving Amy, and he takes her to the Wells museum exhibit and demonstrates the machine, taking her three days into the future. She confirms that fact from a newspaper, but it also, to her horror, reports on her slaying as John's 5th victim.

They go back in time those three days, and plan to prevent the murder of John's 4th victim, now knowing when and where it will occur. But they have a flat tire en route - Herbert calls the police from a pay phone, but they are too late to prevent the murder. They return to Amy's apartment and Herbert leaves to purchase a handgun from a pawnshop. When he returns, the police are waiting for him outside because of his phone call. They take him to the station, and he desperately tries to convince them of Amy's plight. The police finally send a squad car to her apartment, where they find body parts and blood.

Released by the police, Herbert walks the streets in agony. But Amy's voice calls out to him from the shadows - she is held at knife point by John, who demands the key in return for her life.The newspaper was wrong, it was actually an arriving girlfriend who was killed and dismembered. Herbert produces the key, but John reneges and forces Amy to drive him to the museum. Herbert finds another car and, with his limited driving skills, races after them.

Herbert arrives at the exhibit before John can escape and continues to beg for Amy's release. As John enters the time machine, she escapes his grasp. Herbert removes a device from the side of the machine which John realizes is the "vaporizing equalizer" and without it, he'll travel through time, without the machine and any possibility of returning.

Herbert prepares to say goodbye to Amy, but she cannot accept being separated from him, and insists on returning to 1893 to live as his wife.